$\dfrac{ 9m + n }{ -7 } = \dfrac{ -6m - 3p }{ -6 }$ Solve for $m$.
Multiply both sides by the left denominator. $\dfrac{ 9m + n }{ -{7} } = \dfrac{ -6m - 3p }{ -6 }$ $-{7} \cdot \dfrac{ 9m + n }{ -{7} } = -{7} \cdot \dfrac{ -6m - 3p }{ -6 }$ $9m + n = -{7} \cdot \dfrac { -6m - 3p }{ -6 }$ Multiply both sides by the right denominator. $9m + n = -7 \cdot \dfrac{ -6m - 3p }{ -{6} }$ $-{6} \cdot \left( 9m + n \right) = -{6} \cdot -7 \cdot \dfrac{ -6m - 3p }{ -{6} }$ $-{6} \cdot \left( 9m + n \right) = -7 \cdot \left( -6m - 3p \right)$ Distribute both sides $-{6} \cdot \left( 9m + n \right) = -{7} \cdot \left( -6m - 3p \right)$ $-{54}m - {6}n = {42}m + {21}p$ Combine $m$ terms on the left. $-{54m} - 6n = {42m} + 21p$ $-{96m} - 6n = 21p$ Move the $n$ term to the right. $-96m - {6n} = 21p$ $-96m = 21p + {6n}$ Isolate $m$ by dividing both sides by its coefficient. $-{96}m = 21p + 6n$ $m = \dfrac{ 21p + 6n }{ -{96} }$ All of these terms are divisible by $3$ Divide by the common factor and swap signs so the denominator isn't negative. $m = \dfrac{ -{7}p - {2}n }{ {32} }$